How Towel Flipping Holds The Key To The Perfect Pancake Stack

It is literally Christmas time in the Eatosi house. The greatest day of the year is upon us, and here for another food recount with a twist, we learn how towel folding leads to the perfect pancake stack!

With lemon or Nutella, just enjoy.

Jacob E Goodman had a problem. After being tasked with the simple house chore of folding towels, the New York City College mathematician had come a cropper with towel size, moreover running out of space whilst creating piles of towels. Most ordinary people will stack according to dimension; large to small or wide to narrow; Goodman was no different.

Being a mathematician, Goodman proceeded to resolve the problem. The towel flipping conundrum was designed to establish “how many flips would be required to re-organise a disorganised pile of towels”. Of course, Goodman being a mathematician and not wanting to be ridiculed for the rest of his academic career turned to the only viable solution, proceed to write a mathematical paper under a pseudonym and use pancakes, not towels, to prove a mathematical correlation between the two.

Goodman proposed the problem in his paper. ‘The chef in our place is sloppy, and when he prepares a stack of pancakes they come out all different sizes. Therefore, when I deliver them to a customer, on the way to the table I rearrange them (so that the smallest winds up on top, and so on, down to the largest at the bottom) by grabbing several from the top and flipping them over, repeating this (varying the number I flip) as many times as necessary. If there are n pancakes, what is the maximum number of flips (as a function of n) that I will ever have to use to rearrange them?’

Of course, math, being a precise science means that there is no definitive answer. As of yet, there is no answer to the question when the amount of pancakes increases. Bill Gates, yes, the computer whizz, papered his one and only published paper based on a similar conundrum as well as writers from the Simpsons who were specifically trying to ascertain how to re-organise burnt pancakes.

Luckily the religious festivities leading to Shrove Tuesday or Mardi Gras as it’s also known, weren’t as concerned with how you stack, or which sides were burnt.

The tradition of eating pancakes on Shrove Tuesday began as a way to use up ingredients including butter, milk and eggs that were not supposed to be eaten and would go bad during the period of Lent. Pancakes, particularly thin and buttery crepes, were a great way to use up these ingredients in one easy and indulgent dish.

Pancake Day as it is known in the UK has formed part of the cultural landscape in the lead up to the religious festival of lent. In Olney, Buckinghamshire there is an annual pancake race; as so established because in 1445 a woman from the town “heard the shriving bell while she was making pancakes and ran to the church in her apron, still clutching her frying pan. The Olney pancake race is now world famous. Competitors have to be local housewives and they must wear an apron and a hat or scarf.”

Of course the web is laden with recipes for the perfect pancake. The Independent’s guide to ‘the perfect pancake’ can be found here, along with a variety of recipes for fillings. If the American fluffy tall stack pancakes are on your preferred choice, this passed down homemade recipe for AllRecipes.com may just be the answer. The author’s one and only tip if you’re creating either is, get the pan really hot!

Goodman, now in his eighties, has gone on to create a good name for himself in the academic field. His research paper on pancake flipping could however still be one of the most significant to this day. Geneticists use the “flipping” equation to ascertain how many genes would need to be flipped to transform one creatures genetic sequence to another similar bodied animal.

If only there was an equation for the perfect pancake toss, now that would be flipping egg-cellent… (sorry)

Its a flipping conundrum ! I remember Pancake Races from my childhood in the UK and wonder if Pancake make-up got its name from being slapped on with one hand whilst wielding a skillet with the other . The equation brings to mind recent research into how often a dropped piece of toast lands buttered side down. Dog owners will never know !

I should have gone with that as a title! I wondered about that too, Paul, the name that is. It really does not make sense, but the etymology just doesn’t reference anything that was anything but hear say.

Out of curiosity, how often does a buttered side down piece of toast hit the ground?

I love this post – a story about flipping pancakes and the number of towels? I used to love Pancake Tuesday as a child. I really don’t think we had them any other day of the year. The photo you use is gorgeous. Hope you enjoy them this year.

You lost me as soon as you mentioned “n”, but I enjoyed the rest of your essay. I don’t see how the equation accounts for the variable of there being a different number of different sized pancakes in each stack — but there’s a reason I went to law school and not med school. What am I missing??

I never knew why pancakes were traditionally served on Shrove Tuesday…and come to think of it, I didn’t know that eggs and milk weren’t supposed to be eaten during Lent. What DID they eat for those 40 days? Not that this has anything to do with math….

Well, Sharon, this blog is about tenuous links; the story side is there to give you more than just the etymology of pancakes, something else to get your teeth into. What did people eat in the 40 days, mainly vegetables as they were in season and local meats if they could afford it.

Just the other day our local radio station was wondering and debating why IHOP (International House of Pancakes) has free pancakes on Mardi Gras. I wish I had read this before then. Oh well, at least now I know what I’m making for dinner tonight!

Great photo… I had no idea that Mardi Gras was a day to eat pancakes, for the purpose of getting rid of excess ingredients. What a fun fact. I love pancakes. The next time I make them I’ll think about what you’ve written.